I don't really think so. First off, Player Punch
predates Gut Punch
by a fair amount of time. Second, again, they're about different things.
Player punch is an audience reaction trope that covers an event designed to make the player personally invested in the plot - specifically, in getting revenge on the villain or questioning their own, out-of-game morality. Gut Punch
is a single moment in which a work becomes permanently darker. Some player punches are gut punches. Some are not.